Zustandschätzung

Zustandschätzung, often translated as state estimation, is a fundamental concept in many fields of engineering and science. It refers to the process of determining the internal state of a dynamic system based on a series of indirect and potentially noisy measurements. The state of a system is a set of variables that, along with the system's input, completely describe its behavior at any given time. For example, in robotics, the state might include the position and velocity of a robot arm, while in economics, it could represent market indicators.

The core challenge in state estimation lies in the fact that the true state is usually not directly observable. Instead, sensors provide measurements that are functions of the state, but these measurements are subject to errors and uncertainties. Zustandschätzung aims to fuse these imperfect observations with a mathematical model of the system's dynamics to produce an optimal estimate of the true state.

Several algorithms are employed for state estimation, with the Kalman filter and its variants being among the most widely used. The Kalman filter is an optimal recursive algorithm for linear systems with Gaussian noise. For non-linear systems, extensions like the Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF) are utilized. Particle filters are another powerful class of algorithms, particularly effective for highly non-linear and non-Gaussian problems. The goal of these estimators is to minimize the error between the estimated state and the true state, often in a mean-squared error sense. Applications are widespread, including navigation, control systems, financial modeling, and signal processing.